Changes between Initial Version and Version 1 of OfficialTolArchiveNetworkGrzLinModel

Timestamp:

Jan 24, 2011, 5:58:22 PM (15 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkGrzLinModel

@@ +1 @@
+[[PageOutline]]
+
+= Package GrzLinModel =
+
+Max-likelihood and bayesian estimation of 
+[http://en.wikipedia.org/wiki/Generalized_linear_model generalized linear models].
+
+== Weighted Generalized Regresions ==
+
+Abstract class 
+[source:/tolp/OfficialTolArchiveNetwork/GrzLinModel/WgtReg.tol @WgtReg] 
+is the base to inherit weighted generalized linear regressions as poisson, 
+binomial, logit, probit or any other, given just the scalar distribution 
+function [[LatexEquation( F )]] and the corresponding density function 
+[[LatexEquation( f )]]. In a weighted regression each row of input data 
+has a distinct weight in the likelihood function. For example, it can be 
+very usefull to handle with data extrated from an stratified sample.
+
+Let be 
+ * [[LatexEquation( X\in\mathbb{R}^{m\times n} )]] the regression input matrix 
+ * [[LatexEquation( w\in\mathbb{R}^{m} )]] the vector of weights of each register
+ * [[LatexEquation( y\in\mathbb{R}^{m} )]] the regression output matrix 
+ * [[LatexEquation( \beta\in\mathbb{R}^{n} )]] the regression coefficients 
+ * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
+ * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
+ * [[LatexEquation( g )]] the link function
+ * [[LatexEquation( f )]] the density fuciton of a distribution of the 
+[http://en.wikipedia.org/wiki/Exponential_family exponential family]
+
+Then we purpose that the average of the output is the inverse of the link function 
+applyied to the linear predictor
+
+  [[LatexEquation( E\left[y\right]=\mu=g^{-1}\left(X\beta\right) )]]
+